Question

The shortest air column inside a resonator vibrates with a frequency of 250 Hz, if the next harmonic is 750 Hz, and the speed of sound is 343 m/s.

a. Is this resonator closed at one end or open at both ends? Explain.
b. Find the length of the resonator.

Answer 1

Part a)

the two frequencies are in ratio of odd numbers so it must be closed at one end

Part b)

L = 34.3 cm

Step-by-step explanation:

Part a)

Since the shortest frequency is known as fundamental frequency

It is given as

`f_o = 250 Hz`

next higher frequency is given as

`f_1 = 750 Hz`

since the two frequencies here are in ratio of

`(f_1)/(f_o) = (750)/(250) = 3 : 1`

since the two frequencies are in ratio of odd numbers so it must be closed at one end

Part b)

For the length of the pipe we can say that fundamental frequency is given as

`f_o = (v)/(4L)`

here we have

`250 = (343)/(4(L))`

now we will have

`L = (343)/(4* 250)`

`L = 34.3 cm`